Comments on: Better Best Squares & The Future Of Math Textbooks

By: dy/dan » Blog Archive » Pattern Matching In Khan Academy

dy/dan » Blog Archive » Pattern Matching In Khan Academy — Mon, 18 Mar 2013 22:11:05 +0000

[…] diagnoses. That's not to say we shouldn't put machines to work for us. We should. One premise of my work with Dave Major is that the machines should ask rich questions but not assess them, instead sending the responses […]

By: Mg

Mg — Sun, 27 Jan 2013 15:45:34 +0000

I am not sure if this was discussed, but “squareness” is an actual engineering measurement in the area of manufacturing.
It compares the lengths of the diagonals.

http://www.diamondman.com/squareness

By: daily 01/23/2013 « Cshonea’s Blog

daily 01/23/2013 « Cshonea’s Blog — Wed, 23 Jan 2013 20:31:23 +0000

[…] dy/dan » Blog Archive » Better Best Squares & The Future Of Math Textbooks […]

By: Four short links: 22 January 2013 - O'Reilly Radar

Four short links: 22 January 2013 - O'Reilly Radar — Wed, 23 Jan 2013 08:00:34 +0000

[…] Reimagining Math Textbooks (Dan Meyer) — love this outline of how a textbook could meaningfully interact with students, rather than being recorded lectures or PDF versions of cyclostyled notes and multichoice tests. Rather than using a generic example to illustrate a mathematical concept, we use the example you created. We talk about its perimeter. We talk about its area. The diagrams in the margins change. The text in the textbook changes. Check it out — they actually built it! […]

By: VÃ©rot

VÃ©rot — Fri, 18 Jan 2013 09:52:15 +0000

The interface is great, but the positionning of the dot to create the square is rather confusing : the spots are rather big and the point where you click does not correspond to the center of the dot. As a consequence, I made parallelograms instead of squares.

At the beginning, I made several really “not square” squares before realizing this. Which was really disturbing and frustrating.

Reducing the size of the dots or be sure that the point where you click corresponds to the center of the dot would be of great help.

(Maybe it’s a bug, in this case, I’m under Firefox 16.0.1 under Linux)

By: Dave Major

Dave Major — Thu, 17 Jan 2013 16:12:18 +0000

Ah, the perfect mix of exacting criticism and overwhelming joy. Keep it coming!

If anyone does want to try it with a class, please look at http://testing.davemajor.net/squares/teacher/classes as I built in functionality to create your own ‘sandboxed’ version.

By: a different Dave

a different Dave — Thu, 17 Jan 2013 15:13:10 +0000

re: commenter “g”‘s question #3

On that part of the activity, part of the answer is provided already — there is a numerator shown above the box where you can type. That caught me for a moment, too. :)

—-

Has anyone tried this with actual students yet? If you did, tell us everything!

By: Charity

Charity — Wed, 16 Jan 2013 23:11:09 +0000

I can’t wait for this “textbook” to come out for us to use in the classroom. This is the future!!!!!!!!!!!!! Keep up the awesome work.

By: l hodge

l hodge — Wed, 16 Jan 2013 20:55:58 +0000

It is hard for me to separate out the task from the pedagogies.

I like the ability to quickly get and compare first thoughts on a task (rank the squares). I really like the ability to quickly scan and share student explanations.

The interaction between the student and the “book” was at a superficial level in my mind. And where is there problem solving (puzzle) for the students that are not able to generalize the formula?

The page about a square maximizing area was frustrating and didn’t really add insight as to why, or even whether the claim is true. I would not want the program to do all the computations related to the student’s square if it were my class, especially since you are going to ask the students to generalize a formula. It is cumbersome for students to enter in their ideas for a formula which, to me, is the most interesting feature of the lesson.

By: Jason Dyer

Jason Dyer — Wed, 16 Jan 2013 16:21:44 +0000

Big-picture stuff:

This is lovely and the sort of interactivity I want when I think of e-books.

Small-scale specific lesson stuff:

I’m guessing you already were thinking this way, but: it would be a separate lesson prior to this, but it’s totally possible for students to discover the statement “a square encloses the most area for a given perimeter” for themselves and would not be the sort of thing I would just give them (except to make the statement in this one along the lines of “from what we did during the fencing lesson, you know …”)

The constraint ellipse-thing does feel very unintuitive and after I fiddled for a while I could never even get back to the original area my quadrilateral was at (let alone reach an optimal area). I’m unsure what a better approach would be, though.

The “Use these variables to create a best square score for any quadrilateral.” bit is certainly the hardest. First off, the directions are still a little vague, and need something explicit like “use the lengths of the sides a, b, c, d, and the area A” as opposed to “use these variables” (it took me some time to realize the statement meant the variables mentioned in the diagram). Also wrong answers could also use some more feedback beyond “sorry, that’s incorrect”. (Like g up in the comments I was never able to get it to accept my input.) I think in particular I would have loved the page at the end that gave both help and feedback as to what my input gave before I reached the best square score one.

I think the text “How close did our star rating come to predicting our best square score?” could use a little tweaking because as written many students would just put “it’s good” and click on from there. Maybe add a “justify your answer” statement at least?